1÷3=1/(1×3)=1/2×(1/1-1/3)
1/3÷5=1/(3×5）=1/2×(1/3-1/5)
1/5÷7=1/(5×7）=1/2×(1/5-1/7)
……
1÷3＋1/3÷5＋1/5÷7＋1/7÷9＋1/9÷11＋1/11÷13＋1/13÷15
=1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9）+1/(9×11)+1/(11×13)+1/(13×15)
=1/2×（1/1-1/3+1/3-1/5+1/5-1/7+……+1/13-1/15）
=1/2×（1-1/15）
=7/15